EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                       RULE 13a-14(b) UNDER THE SECURITIES
                       EXCHANGE ACT OF 1934 AND 18 U.S.C.
                      SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



      In connection with the quarterly report of Syms Corp (the "Company") on
Form 10-Q for the period ended November 27, 2004, as filed with the Securities
and Exchange Commission on the date hereof (the "Report"), I, Marcy Syms, Chief
Executive Officer of the Company, certify, to the best of my knowledge, pursuant
to Rule 13a-14(b) under the Securities and Exchange Act of 1934 and 18 U.S.C.
ss. 1350, as adopted pursuant to ss. 906 of the Sarbanes-Oxley Act of 2002,
that:

            (1)   The Report fully complies with the requirements of Section
13(a) or 15(d) of the Securities Exchange Act of 1934; and

            (2)   The information contained in the Report fairly presents, in
all material respects, the financial condition and results of operations of the
Company.




                                       /s/ Marcy Syms
                                       -----------------------
                                       Marcy Syms
                                       Chief Executive Officer
                                       Syms Corp
                                       January 6, 2005


A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the electronic version of this written statement
required by Section 906, has been provided to the Company and will be retained
by the Company and furnished to the Securities and Exchange Commission or its
staff upon request.